Bunuel wrote:

In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

A. 21/100

B. 1/10

C. 1/8

D. 3/10

E. 4/5

TOTAL number of cheaters = (

# of people who cheated AND got caught) + (

# of people who cheated AND DID NOT get caught)

To make things easier, let's say there are 100 people in the math class.

Let x = TOTAL number of cheaters

one-tenth of the students cheated on a test and were caught1/10 of 100 = 10, so

10 people cheated AND got caughtone-fifth of the students who cheated did not get caughtIn other words, 1/5 of x = number of students who cheated and DID NOT get caught

Rewrite as:

0.2x = number of students who cheated and DID NOT get caughtPlug all values into original equation: TOTAL number of cheaters = (

# of people who cheated AND got caught) + (

# of people who cheated AND DID NOT get caught)

We get; x =

10 +

0.2xSubtract 0.2x from both sides: 0.8x = 10

Solve: x = 12.5

What fraction of the class cheated on the test?If there are 100 people in the class, and 12.5 of them cheated, then the fraction of the class who cheated on the test = 12.5/100 = 1/8

Answer:

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com

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